The view of [1]} and [2]} of defining probability measures on a manifold makes use of a direct parameterization. The method in this paper only assumes that one knows a continuously differentiable constraint function \(g\)  that determines the manifold, which is useful for cases where a direct parameterization is not known. We show, in Section , that the need for a parameterization may be further circumvented by approximating the explicit form of the CGFD using Markov chain Monte Carlo (MCMC) methods.
